Zero inflated negative binomial-generalized exponential distributionand its applications

Abstract

In this paper, we propose a new zero inflated distribution, namely, the zero inflated negative binomial-generalized exponential (ZINB-GE) distribution. The new distribution is used for count data with extra zeros and is an alternative for data analysis with over-dispersed count data. Some characteristics of the distribution are given, such as mean, variance, skewness, and kurtosis. Parameter estimation of the ZINB-GE distribution uses maximum likelihood estimation (MLE) method. Simulated and observed data are employed to examine this distribution. The results show that the MLE method seems to have high efficiency for large sample sizes. Moreover, the mean square error of parameter estimation is increased when the zero proportion is higher. For the real data sets, this new zero inflated distribution provides a better fit than the zero inflated Poisson and zero inflated negative binomial distributions.

Keywords

• overdispersion
• zero inflated distribution
• count data with extra zeros
• random variate generation
• MLE